Suppression of finite-size effects in one-dimensional correlated systems

TL;DR

This paper demonstrates that applying a specific non-uniform deformation to 1D quantum systems suppresses finite-size effects, making open systems behave like periodic ones, with confirmed results in correlated models like the extended Hubbard model.

Contribution

The study introduces a deformation method that eliminates leading finite-size corrections in 1D quantum systems, aligning open boundary results with periodic boundary conditions.

Findings

For m ≥ 2, the 1/N correction to ground state energy vanishes.

At m=2, open boundary systems match periodic boundary systems.

Numerical confirmation in extended Hubbard and free-Fermion models.

Abstract

We investigate the effect of a non-uniform deformation applied to one-dimensional (1D) quantum systems, where the local energy scale is proportional to $g_j = [\sin (j \pi / N)]^m$ determined by a positive integer $m$, site index $1 \leq j \leq N-1$, and the system size N. This deformation introduces a smooth boundary to systems with open boundary conditions. When $m \geq 2$, the leading $1/N$ correction to the ground state energy per bond $e_0^{(N)}$ vanishes and one is left with a $1/N^2$ correction, the same as with periodic boundary conditions. In particular, when $m = 2$, the value of $e_0^{(N)}$ obtained from the deformed open-boundary system coincides with the uniform system with periodic boundary conditions. We confirm the fact numerically for correlated systems, such as the extended Hubbard model, in addition to 1D free-Fermion models.